July 20, 2005

Workshops Day 2

It's lunchtime at StreetFest, so I'll take the opportunity to post a bit about what's been going on!John Baez kicked off the day with a talk on higher dimensional gauge theory. The basic idea here seems to be that you figure out what happens when particles move around on a manifold with odd curvature. The interesting thing is that it is no longer possible to compare, say, two vectors but it is only possible to compare them relative to some path which brings them together. The other cool thing I found out about is something called a "thin homotopy". This is just like Ye Olde Homotopy, except that it sweeps out no area. For instance a homotopy which only does stuff like backtracking along a path is a thin homotopy. Working modulo thin homotopies seems to be the thing to do in this area. Anyway, the slides from the talk are up here.

After that there was a really fun talk by Timothy Porter, who has a wonderful sense of mathematical humour! He was speaking about topological quantum field theories and I managed to follow along a bit and see what manifolds and cobordisms have to do with braided monoidal categories. Neat stuff!

Next up was Andrey Lazarev who spoke about graph cohomology. I don't really understand this stuff so I won't say any more.

In between the talks I had some nice discussions with category theorists about higher dimensional rewriting, noncommutative logic and that sort of jazz. I'll probably hang around at Streetfest for the rest of today and tomorrow - this post will be updated later with the afternoon's talks. Mayhaps someone else will blog details of the philosophy workshop...

Update (26/7): Not many more of the talks were logic related so I decided to stop posting details.